Superlinear perturbations of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential

Abstract

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when $\lambda$ is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.

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